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- Imaginary and Complex Numbers

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There are times when we are interested in obtaining a better understanding of the properties of a complex number, such as its argument and modulus. In this section, we will learn how to calculate the argument, also known as the angle, and the modulus, also known as the magnitude or the absolute value, of a complex number.

Basic Concepts: Distance formula: $d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$, Solving expressions using 45-45-90 special right triangles

Related Concepts: Imaginary zeros of polynomials, Magnitude of a vector, Direction angle of a vector

Notes:

Magnitude = modulus = absolute value $|z|= \sqrt{a^2+b^2}$

Argument = angle $arg(z)=\theta$

Magnitude = modulus = absolute value $|z|= \sqrt{a^2+b^2}$

Argument = angle $arg(z)=\theta$

- 1.Given the complex number $z=2+3i$

a)Find its absolute valueb)Find the angle it makes in the complex plane in radians - 2.Given the complex number $w=5i-3$

a)Find its modulusb)Find its argument in radians - 3.Given that a complex number $w$ makes an angle $\theta=\frac{3\pi}{4}$ in the complex plane and has an absolute value $|w|=5$, write the complex number w in rectangular form.

49.

Imaginary and Complex Numbers

49.1

Introduction to imaginary numbers

49.2

Complex numbers and complex planes

49.3

Adding and subtracting complex numbers

49.4

Complex conjugates

49.5

Multiplying and dividing complex numbers

49.6

Distance and midpoint of complex numbers

49.7

Angle and absolute value of complex numbers

49.8

Polar form of complex numbers

49.9

Operations on complex numbers in polar form

We have over 2320 practice questions in ACCUPLACER Test Prep for you to master.

Get Started Now49.1

Introduction to imaginary numbers

49.2

Complex numbers and complex planes

49.3

Adding and subtracting complex numbers

49.4

Complex conjugates

49.5

Multiplying and dividing complex numbers

49.6

Distance and midpoint of complex numbers

49.7

Angle and absolute value of complex numbers

49.8

Polar form of complex numbers

49.9

Operations on complex numbers in polar form